Before resonators, such as piezo-resonators, are formed, ingots of Si (silicon) are manufactured that are doped with large amounts of impurities, such as n-type dopants like P (phosphorus), for example. Then, a plurality of wafers are cut out from these ingots, and resonators are formed in a plurality of zones defined on the wafers. Thereafter, the respective zones are cut along the outlines of the respective zones of the wafers to thereby form resonance devices.
The ingots of Si are manufactured substantially in cylindrical shapes by the growth of single-crystalline Si according to, for example, a manufacturing method referred to as a CZ method (Czochralski method). For example, the ingots are manufactured by melting, on heating, polycrystalline Si doped with large amounts of n-type dopant, for example, such as P, and immersing Si rods in the molten Si, and lifting the Si rods while rotating the rods.
Patent Document 1: Japanese Patent Application Laid-Open No. 2010-028536.
It has been determined that these ingots each have a higher impurity concentration at the outer peripheral side in a radial direction of the ingot than at the inner peripheral side therein. At the same time, these ingots also have a higher impurity concentration at the bottom side in a lifting direction of the ingot than the top side therein. In accordance with these distributions in impurity concentration, the ingots each have a resistivity distribution formed to decrease in resistivity from the inner peripheral side toward the outer peripheral side, and a resistivity distribution formed to decrease in resistivity from the top side toward the bottom side.
Moreover, when a plurality of wafers are cut out from the ingots that have such distributions in resistivity, the resistivity varies among the wafers, depending on the distributions in impurity concentration. When resonators are manufactured from these wafers, frequency temperature characteristics vary depending on the variation in resistivity among the wafers. However, conventionally, this variation in resistivity among wafers have not been addressed at all.